The long-range nature of the effect of a pump or a battery on an interacting diffusive fluid is discussed. It is shown that off criticality the pump generates long-range modulation in the density profile of the form of a dipolar electric potential and a current profile in the form of a dipolar electric field. The density profile is drastically modified when the fluid is at its critical point:...
The shift of the position of a front found by Bramson in the case of the Fisher-KPP equation is modified at the transition between pulled and pushed fronts. Based on an exactly solvable case, one can predict the cross-over function which determines this shift near this transition. The correction due to a cut-off is also modified at this transition. This raises the question of whether the...
Stationary non equilibrium states (SNS) have a rich and complex structure. The large deviations rate functionals for the empirical measure of a few one dimensional SNS of stochastic interacting systems have been computed, among wich the exclusion process and the Kipnis-Marchioro-Presutti (KMP) model. The corresponding rate functionals are not local due to the presence of long range...
Single-file diffusion with a defect particle is fundamental to the understanding of driven tracers in narrow channels. In this talk, two variations on the simple exclusion process on a ring geometry are considered as minimal models of such a setup. The first variation is a totally asymmetric tracer in a bath of symmetric particles. The second variation is a defect particle with priority in a...
Single-file transport, where particles diffuse in narrow channels while not overtaking each other, is a fundamental model for the tracer subdiffusion observed in confined systems, such as zeolites or carbon nanotubes. This anomalous behavior originates from strong bath-tracer correlations in 1D, which have however remained elusive, because they involve an infinite hierarchy of equations....
We describe an approach to the Toda lattice relying only on basis facts of linear algebra, making no use of symplectic geometry. This approach is due to Leite et al, and has many advantages, particularly to the analysis of the long-time behavior of solutions of the Toda lattice.
Integrable many-particle systems arise in wide variety. To illustrate their generalized hydrodynamics, the Calogero fluid will be used as prime example. The fluid consists of classical particles moving on the line and interacting through the repulsive 1/sinh^2 pair potential. Discussed are generalized Gibbs ensembles, the corresponding random Lax matrix, its density of states, and GGE averaged...
Over the past 30 years, the hydrodynamic limit has been proved for many interacting particle systems. However, there are still many models for which rigorous proofs are missing, especially those called non-gradient models. Also, most of the existing results are for models on Z^d lattices with one conserved quantity. There has been no theory of how much existing theories can be generalized, and...
Evaluating fluctuations and correlations at large scales of space and time in quantum and classical many-body systems, in and out of equilibrium, is one of the most important problems of emergent physics. I will explain how basic hydrodynamic principles give access to exact results at the ballistic scale, solely from the data of the Euler-scale hydrodynamic equations of the many-body system....
In this talk, I will present a model which was introduced in [1] and
consists of an exclusion process with different types of particles,
let us say types A, B, and C. Depending on the interaction rate
between different types of particles, the limiting fluctuations end up
in different universality classes: either the fluctuations are
governed by energy solutions of the stochastic Burgers...
The macroscopic fluctuation theory (MFT) is a consistent and self-contained description of macroscopic fluctuations using
only transport coefficients. In the formulation of the Rome group an important motivation was the discovery that we could reproduce by a purely macroscopic calculation the result of Derrida, Lebowitz and Speer obtained solving the microscopic symmetric simple exclusion...
The large deviations for the diffusion of a tracer in a 1D time dependent medium can be described, on diffusive scales,
by the macroscopic fluctuation theory (MFT).
The corresponding MFT variational equations are mapped to the integrable derivative non-linear Schrodinger
equation. We provide a solution using inverse scattering methods, and obtain the large deviation rate function
for the...
For any stochastic time-series of duration T, the time t_max at which
the process achieves its maximum is an important observable. For example,
for a stock price over a trading period T, one would like to sell the
stock at the time when the price is maximal. I'll discuss the statistics
of t_max for a variety of stochastic processes. In particular, for a large class
of stationary...
To derive a macroscopic description of a system (in terms of
hydrodynamical fields), starting from a microscopic one (in terms of
interacting particles), the usual route introduces an intermediate
kinetic equation, and takes advantage of the difference of time scales
between fast and slow modes to set up a Chapman-Enskog expansion. When
finite size effects are important at the macroscopic...
The “Brownian bees” model, suggested by J. Berestycki, E. Brunet, J. Nolen, and S. Penington, is a new member of a family of Brunet-Derrida particle systems which mimic some aspects of biological selection. Like other Brunet-Derrida systems, the Brownian bees can be also considered as a system of interacting particles with reset. The model describes an ensemble of N independent branching...
